Question

Mimi plans on growing tomatoes in her garden. She has 15 cherry tomato seeds. Based on her experience, the probability of a seed turning into a seedling is 0.30.

(a) Let X be the number of seedlings that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

(b) Find the probability that she gets at least 5 cherry tomato seedlings. (Round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit.

Answer 1

Mimi plans on growing tomatoes in her garden. She has 15 cherry tomato seeds. Based on her experience, the probability of a seed turning into a seedling is 0.30.

(a) Let X be the number of seedlings that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

For binomial probability distribution,

Binomial Formula. Suppose a binomial experiment consists of n trials and results in x successes. If the probability of success on an individual trial is P, then the binomial probability is:

b(x; n, P) = _nC_x * P^x * (1 - P)^{n - x}
or
b(x; n, P) = { n! / [ x! (n - x)! ] } * P^x * (1 - P)^{n - x}

Notation

The following notation is helpful, when we talk about binomial probability.

• x: The number of successes that result from the binomial experiment.
• n: The number of trials in the binomial experiment.
• P: The probability of success on an individual trial.
• Q: The probability of failure on an individual trial. (This is equal to 1 - P.)
• n!: The factorial of n (also known as n factorial).
• b(x; n, P): Binomial probability - the probability that an n-trial binomial experiment results in exactly x successes, when the probability of success on an individual trial is P.
• _nC_r: The number of combinations of n things, taken r at a time.

Here, the number of trials (n) = number of cherry tomato seeds = 15

Probability of successes (p) = probability of a seed turning into a seedling = 0.30

Probability of failures (q) = 1-p = 1-0.30 = 0.70

(b) Find the probability that she gets at least 5 cherry tomato seedlings.

P(X5) = 1-P(X<5)

Now,

P(X<5) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

Therefore, P(X5) = 1-P(X<5) = 1-0.51549105922=0.48450894078=0.485 (To 3 decimal places)

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