Question

1. The table to the right depicts the results of a survey
of 300 random adults as to what their favorite type of
pet is.

	Cat	Dogs	Others	Total
Women	94	66	30	190
Men	42	58	20	120
Total	136	124	50	310

1a. If one person is selected at
random from the group, what is the probability that the person answered was a woman, given
that the person prefers dogs as a pet?

____________________

1b. What is the probability that a person selected at random from the group is either
a man or prefers something other as a pet?

______________________

1c. If one of the subjects is randomly selected, find the probability that the person
prefers cats as a pet, given that the person is a woman.

______________________

2. Calculate ₁₄C₁₁ , using the formal formula (not the permutation or combination

commands on your calculator). Show work.

Answer 1

1a) P(Women | dog) = 66/124 = 33/62 = 0.5323 (approx)

So, the probability that the person answered was a woman given that the person prefers dogs /as pet is 33/62 or 0.5323.

1b) P(man or others as pet) = (120+30)/310 = 15/31 = 0.4839 (approx)

So, the probability that the person selected at random from the group is either a man or prefers something other as a pet is 15/31 or 0.4839.

1c) P(cat | woman) = 94/190 = 47/95 = 0.4947 (approx)

So, the probability that the person prefers cats as a pet, given that the person is a woman is 47/95 or 0.4947.

2). - 14 14 * 13 * 12 * 11! 11! * 3! 14 * 13 * 12 -= 364 4114 1111! * (14 - 11)!

So, 364 is the answer.

Formula used:

n! nop=!*(n-r)!