a.) Complete the tree diagram,
As given in the diagram,
Probability for bag 1, P(B1) = 0.35,
Probability for bag 2, P(B2) = 0.45,
We know that sum of all the probabilities for any event is always 1. Thus,
P(B1) + P(B2) + P(B3) = 1,
0.35 + 0.45 + P(B3) = 1,
0.80 + P(B3) = 1,
P(B3) = 1- 0.80 = 0.20.
Therefore, the probability of bag 3, P(B3), is 0.20.
b.) Work out the probability that a player will select a red ball,
The probability that a player will select a red ball =
probability that a player will select bag1 and a red ball
+ probability that a player will select bag2 and a red ball
+ probability that a player will select bag3 and a red ball
probability that a player will select bag1 and a red ball
= probability of selecting bag 1 x probability of selecting a red ball
= 0.35 x 0.60
= 0.21
probability that a player will select bag2 and a red ball
= probability of selecting bag 2 x probability of selecting a red ball
= 0.45 x 0.20
= 0.09
probability that a player will select bag3 and a red ball
= probability of selecting bag 3 x probability of selecting a red ball
= 0.20 x 0.70
= 0.14
Thus, The probability that a player will select a red ball = 0.21 + 0.09 + 0.14 = 0.44
Therefore, The probability that a player will select a red ball is 0.44.
c.) the same player is going to play the game 200 times consecutively. the number of black balls he should expect to pick,
The probability that a player will select a black ball
= 1 - The probability that a player will select a red ball
= 1 - 0.44 = 0.56
the number of black balls he should expect to pick
= probability that a player will select a black ball x Number of trials
= 0.56 x 200 = 112
Therefore, if the same player is going to play the game 200 times consecutively. the number of black balls he should expect to pick 112 balls.
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