A coin has a probability of 1/4 for head, and is repeatedly tossed until we throw...

A coin has a probability of 1/4 for head, and is repeatedly tossed until
we throw head. The successive results of the toss are independent of each other.
What is the probability that the first time we throw head after an odd number of toss?
Hint: Use the law of total probability and consider the event that the
first toss is head is, and her complement, as conditioning events.

Correct answer: 3/7

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A fair coin is tossed until a head appears. Given that the first head appeared on...

A fair coin is tossed until a head appears. Given that the first head appeared on an even-numbered toss, find the probability that it occurred on the second or the fourth toss.

A biased coin (P(head) = p , p is not equal to 0.5) is tossed repeatedly....

A biased coin (P(head) = p , p is not equal to 0.5) is tossed repeatedly. Find the probability that there is a run of r heads in a row before there is a run of s tails, where r and s are positive integers. Express the answer in terms of p, r and s.

A coin is tossed repeatedly until heads has occurred twice or tails has occurred twice, whichever...

A coin is tossed repeatedly until heads has occurred twice or tails has occurred twice, whichever comes first. Let X be the number of times the coin is tossed. Find: a. E(X). b. Var(X).

A fair coin is tossed until the first head occurs. Do this experiment T = 10;...

A fair coin is tossed until the first head occurs. Do this experiment T = 10; 100; 1,000; 10,000 times in R, and plot the relative frequencies of this occurring at the ith toss, for suitable values of i. Compare this plot to the pmf that should govern such an experiment. Show that they converge as T increases. What is the expected number of tosses required? For each value of T, what is the sample average of the number of...

A coin with P(head) = 2/3 is tossed six times (independently). What is the probability of...

A coin with P(head) = 2/3 is tossed six times (independently). What is the probability of obtaining exactly four CONSECUTIVE heads or exactly five CONSECUTIVE heads?

A fair coin is flipped repeatedly. (a) (6pts) Suppose we hope that with probability at least...

A fair coin is flipped repeatedly. (a) (6pts) Suppose we hope that with probability at least 0.9 the frequency of heads showing up is between 0.4 and 0.6. Use Chebyshev’s inequality to estimate at least how many times the coin should be flipped. (b) (6pts) Suppose we hope that with probability at least 0.95 the frequency of heads showing up is between 0.4 and 0.6. Use the central limit theorem to estimate at least how many times the coin should...

1. A fair coin is tossed twice. Consider the following events: a) A = a head...

1. A fair coin is tossed twice. Consider the following events: a) A = a head on the first toss; b) B = a tail on the first toss; c) C = a tail on the second toss; d) D = a head on the second toss. Are events A and B mutually exclusive ? WHY or WHY NOT ? Are events C and D Independent ? WHY or WHY NOT ? 2. Suppose there are 3 similar boxes. Box...

1. A coin is tossed 100 times, each resulting in a tail (T) or a head...

1. A coin is tossed 100 times, each resulting in a tail (T) or a head (H). If a coin results in a head, Roy have to pay Slim 500$. If the coin results in a tail, Slim have to pay Roy 500$. What is the probability that Slim comes out ahead more than $20,000?

A coin is tossed thrice. Find the probability of getting

A coin is tossed thrice. Find the probability of getting (i) exactly two heads. (ii) at least two tails.

A fair coin will be tossed three times. (a) Indicating a head by H and a...

A fair coin will be tossed three times. (a) Indicating a head by H and a tail by T write down the outcome space. (b) What is the probability that on the first toss the outcome with a tail? (c) What is the probability of obtaining exactly two heads from the three coin tosses? (d) What is the probability that the first toss gives a tail and exactly two heads are obtained from the three coin tosses? Are the outcomes...

Subjects