Question

A box of candy hearts contains 52 hearts of which 19 are white, 10are tan, 7 are pink, 3 are purple, 5 are yellow, 2 are orange, and6 are green. If you select 9 pieces of candy randomly from the box,without replacement, give the probability thata) three of the hearts are white.b) three are white, two are tan, one is pink, one is yellow, andtwo are green.

Answer 1

Answer:

a. 0.2917

b. 0.00622

Step-by-step explanation:

Since the question deals with selection, we use the combination formula to derive the probability.

Total number of cards = 52.

White = 19, Tan =10, Pink =7, Purple = 3, Yellow = 5, Orange = 2, Green = 6

for question a, to determine the probability of exactly 3 Hearts being White:

i. we find the number of ways to choose 3White hearts from Possible 19, i.e 19C3

ii. We find the number of ways ro choose the remaining 6 hearts randomly from the possibility 33 remaining i.e 33C6

iii. We find the number of ways 9 hearts could be chosen generally from 52 hearts. i.e 52C3

So our Probability equation becomes:

Number of expected outcome/number of actually possible outcome.

Expected outcome = 19C3 * 33C6

Possible outcome = 52C9

Hence, Probability of choosing 3hearts without replacement

=[19C3 * 33C6]/ 52C9

= [969 * 1107568]/3679075400

=0.2917.

For question b, To choose 3white, 2tan, 1pink, 1yellow and 2green, we follow the same steps as above.

Number of ways to choose 3white From 19 = 19C3

Number of ways to choose 2tan From 10 = 10C2

Number of ways to choose 1pink From 7= 7C1

Number of ways to choose 1yellow From 5 = 5C1

Number of ways to choose 2green From 6= 6C2

Number of possible ways to actually choose 9 cards from 52 = 52C9

Probability equation = expected outcome/possible outcome.

Expected outcome = 19C3 * 10C2 * 7C1 * 5C1 * 6C2

Possible outcome = 52C9

Probability of 3white, 2tan, 1pink, 1yellow, 2green =

= [19C3 * 10C2 * 7C1 * 5C1 * 6C2]/52C9

= [969*45*7*5*15]/3679075400

=0.00622