Answer:
a. Probability of Pulling one of each = 0.03175
b. Probability of Pulling 4 Honey Crisp = 0.001797
Probability of 2 G.Smith = 0.1144
Probability of 1 Red Delicious = 0.4559
Step-by-step explanation:
Given
Granny Smiths = 23
Honey Crisp = 14
Red Delicious = 31
Required
- Probability of Pulling out one of each
- Probability of Pulling out 4 Honey Crisp; 2 Granny Smiths; 1 Red Delicious
First, the total number of apple needs to be calculated.
Total = Granny Smiths + Honey Crisp + Red Delicious
Total = 23 + 14 + 31
Total = 68
Probability of Pulling 1 of each
= P(Granny Smiths) and P(Henry Ford) and P(Red Delicious)
- Granny Smiths;
This is calculated by dividing number of Granny Smiths apples by total number of apples.
Probability = 23/68
Similarly,
Probability of Pulling Honey Crisp= Number of Honey Crisp divided by total
Probability = 14/68
Probability = 7/34
Probability of Pulling Red Delicious = Number of Red Delicious divided by total
Probability = 31/68
So, Probability of Pulling 1 of each = 23/68 * 7/34 * 31/68
Probability = 4991/157216
Probability = 0.03175
Probability of Pulling out 4 Honey Crisp;
= P(Honey) * P(Honey) * P(Honey) * P(Honey)
= (P(Honey))⁴
= (7/34)⁴
= 2401/1336336
= 0.001797
Probability of Pulling 2 Granny Smiths;
= P(Granny) * P(Granny)
= (P(Granny))²
= (23/68)²
= 529/4624
= 0.1144
Probability of 1 Red Delicious
= number of red delicious divided by total
= 31/68
= 0.4559
(only 45 athletes left).