Daughter: Dad, I think your candidate is going to lose today\'s primaries. Fathe

Question

Daughter: Dad, I think your candidate is going to lose today's primaries.

Father: Nonsense, There are 3 states voting today. Her opponent has a 60% chance to win each of them. But that means his chance of winning all 3 is 60% of 60% of 60%, which is 21.6%. Since probabilities have to sum to 100% and there are only 2 people running my candidate has a 78.4% chance of winning all 3 states.

Assuming the state elections are independent, what is the correct probability for the dad in the comic's candidate winning the primary?

Explanation / Answer

Solution-

Since her opponent has a 60% chance to win each of them, so there is 40% of his chance winning a state.

Thus, correct chance of winning all three states would be -

0.4 * 0.4 * 0.4

= 0.064

= 6.4%

Answer

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