Question

1. A probability experiment is conducted. Which of the following cannot be considered a probability of an outcome? 1) 0.23 2) 1.00 3) - 0.34 4) 0.05

b- In a scientific study there are eight guinea pigs, five of which are pregnant. If three are selected at random without replacement, find the probability that all three are pregnant. P(all three are pregnant) =

Answer 1

Solution :

1) The probability of an outcome can have any value between 0 and one (both inclusive).

Hence, -0.34 cannot be considered a probability of an outcome.

b) Total number of guinea pigs = 8

Number of pregnant pigs = 5

Three guinea pigs are selected at random without replacement.

Probability that first selected guinea pig is pregnant = 5/8

Now, since the pigs are selected without replacement, one guinea pig is already selected, therefore we are left with total 7 guinea pigs in which 4 are pregnant.

Probability that second selected pig is pregnant = 4/7

Now, since the pigs are selected without replacement and two guinea pigs are already selected, therefore we are left with total 6 guinea pigs in which 3 are pregnant.

Probability that third selected guinea pig is pregnant = 3/6

Using multiplication theorem of probability we get,

P(all three are pregnant) = (5/8) × (4/7) × (3/6)

P(all three are pregnant) = (5/28)

The probability that all three are pregnant is 5/28.