Math  /  Data & Statistics

QuestionA certain species of animal has a 25\frac{2}{5} probability of any one offspring being male and a 35\frac{3}{5} probability of any one offspring being female. Fill in the remaining probabilities on the tree diagram and use that information to find the probability that an adult female of the species produces three offspring that are all males, given that the first is a male.
Choose the correct tree below. A. B. C. w an example Get more help - Clear all Final check

Studdy Solution

STEP 1

1. The probability of any one offspring being male is 25 \frac{2}{5} .
2. The probability of any one offspring being female is 35 \frac{3}{5} .
3. The events are independent, meaning the probability of each offspring being male or female is the same regardless of previous outcomes.

STEP 2

1. Understand the tree diagram structure.
2. Calculate the conditional probability of three male offspring given the first is male.
3. Identify the correct tree diagram.

STEP 3

Understand the tree diagram structure. Each branch represents the probability of an offspring being male (M) or female (F). The first level of branches represents the first offspring, the second level represents the second offspring, and the third level represents the third offspring.

STEP 4

Given that the first offspring is male, the probability of this event is 25 \frac{2}{5} .

STEP 5

Calculate the probability that the second offspring is male. Since the events are independent, this probability is also 25 \frac{2}{5} .

STEP 6

Calculate the probability that the third offspring is male. Again, since the events are independent, this probability is 25 \frac{2}{5} .

STEP 7

Calculate the overall probability of three male offspring given the first is male. Multiply the probabilities of each independent event:
P(3 males | first is male)=(25)×(25)×(25)=8125P(\text{3 males | first is male}) = \left(\frac{2}{5}\right) \times \left(\frac{2}{5}\right) \times \left(\frac{2}{5}\right) = \frac{8}{125}

STEP 8

Identify the correct tree diagram. The correct diagram will show the probability paths for M, M, M with probabilities 25 \frac{2}{5} , 25 \frac{2}{5} , and 25 \frac{2}{5} respectively for the second and third offspring.
The probability that an adult female produces three male offspring, given the first is male, is:
8125 \boxed{\frac{8}{125}}

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