Answer:
Let's calculate the probabilities step by step:
P(neither 6): This means neither spinner A nor spinner B shows a 6. To calculate this probability, you multiply the probabilities of both events not showing a 6.
P(neither 6 on A and B) = P(neither 6 on A) * P(neither 6 on B)
P(neither 6 on A) = 1 - P(6 on A) = 1 - 0.3 = 0.7
P(neither 6 on B) = 1 - P(6 on B) = 1 - 0.45 = 0.55
P(neither 6 on A and B) = 0.7 * 0.55 = 0.385
So, the probability of neither spinner A nor spinner B showing a 6 is 0.385.
P(only one 6): This means exactly one of the spinners shows a 6. To calculate this probability, you need to consider two cases:
a) Spinner A shows a 6, and Spinner B does not.
b) Spinner A does not show a 6, and Spinner B shows a 6.
P(only one 6) = P(6 on A and not 6 on B) + P(not 6 on A and 6 on B)
P(6 on A and not 6 on B) = P(6 on A) * P(not 6 on B)
P(not 6 on A and 6 on B) = P(not 6 on A) * P(6 on B)
P(6 on A and not 6 on B) = 0.3 * (1 - 0.45) = 0.3 * 0.55 = 0.165
P(not 6 on A and 6 on B) = (1 - 0.3) * 0.45 = 0.7 * 0.45 = 0.315
P(only one 6) = 0.165 + 0.315 = 0.48
So, the probability of getting exactly one 6 is 0.48.
P(6 on spinner B only): This means that only spinner B shows a 6. To calculate this probability, you need to consider two cases:
a) Spinner A does not show a 6, and Spinner B shows a 6.
P(6 on B only) = P(not 6 on A and 6 on B) = (1 - 0.3) * 0.45 = 0.7 * 0.45 = 0.315
So, the probability of getting a 6 on spinner B only is 0.315.
Explanation:
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