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
