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Answer:
The probability that the coin landed heads given that a white ball is selected is 0.3957.
Step-by-step explanation:
Let W = a white ball is selected.
Balls in Urn A = 3 white and 8 red = 11 balls.
Balls in Urn B = 10 white and 14 red = 24 balls.
A coin is tossed to select an urn.
If the coin turns up Heads urn A is selected and if it turns up Tails urn B is selected.
P (A) = P(B) = 0.50
Compute the probability that a white ball is selected as follows:
P (W) = P (W ∩ A) + P(W ∩ B)
= P (White from A)×P (A) + P (White from B)×P (B)
[tex]=[\frac{3}{11}\times0.50]+[\frac{10}{24}\times0.50] \\=0.1364+0.2083\\=0.3447[/tex]
The probability of selecting a white ball is P (W) = 0.3447.
If the coin lands Heads it implies that urn A was selected.
Then compute the probability that urn A is selected given that a white ball was selected as follows:
[tex]P(A|W)=\frac{P(W\cap A)}{P(W)}=\frac{\frac{3}{11} \times0.50}{0.3447} =0.3957[/tex]
Thus, the probability that the coin landed heads given that a white ball is selected is 0.3957.
The probability that the coin landed heads given that a white ball is selected is 0.3957.
Let W = a white ball is selected.
Balls in Urn A = 3 white and 8 red = 11 balls.
Balls in Urn B = 10 white and 14 red = 24 balls.
What is the conditional probability?
Conditional probability is the probability of one event occurring with some relationship to one or more other events.
A coin is tossed to select an urn.
When coin is tossed the we get either head or tail.
Therefore,If the coin turns up Heads urn A is selected and if it turns up Tails urn B is selected.
P (A) = P(B) = 0.50
Firstly. we have compute the probability that a white ball is selected as follows
P (W) = P (W ∩ A) + P(W ∩ B)
= P (White from A)×P (A) + P (White from B)×P (B)
[tex]=\frac{3}{11}(0.50)+\frac{10}{24}(0.50) \\=0.1364+0.2083\\=0.3447[/tex]
The probability of selecting a white ball is P (W) = 0.3447.
If the coin lands Heads it implies that urn A was selected.
Then compute the probability that urn A is selected given that a white ball we use the formula for conditional probability
P(A/W)=P(W∩A)/P(W)
[tex]=\frac{3/11(0.50)}{0.3447}[/tex]
[tex]=0.3957[/tex]
Thus, the probability that the coin landed heads given that a white ball is selected is 0.3957.
To learn more about the probability visit:
https://brainly.com/question/24756209
