Suppose we roll a die and let A be the event that the number of spots showing on the die is 6.
We then toss a coin and let B be the event that the coin comes up heads.
Then, P (A and B) is ____.

The two events described (rolling a die & getting a 6 and tossing a coin & the coin comes up heads), are independent events. The chances of one occurring doesn't affect/depend on the chances of the other happening.

And for independent events, mathematically, P(A and B) = P(A n B) = P(A) × P(B)

P(A) = (1/6)

P(B) = (1/2)

(We've assumed the die and the coin are fair; each sample point with an equal probability of occurring)

P(A and B) = (1/6) × (1/2) = (1/12)

Suppose we roll a die and let A be the event that the number of spots showing on the die is 6. We then toss a coin and let B be the event that the coin comes up heads. Then, P (A and B) is ____.

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Suppose we roll a die and let A be the event that the number of spots showing on the die is 6.
We then toss a coin and let B be the event that the coin comes up heads.
Then, P (A and B) is ____.