SOLUTION: 1. A coin is tossed thrice. What is the probability that at least 2 heads occur? 2. A pair of dice is rolled. What is the probability that the sum is equal to: a. 5 b. 10 3.

Question 71536: 1. A coin is tossed thrice. What is the probability that at least 2 heads occur?
2. A pair of dice is rolled. What is the probability that the sum is equal to:
a. 5
b. 10
3. If a card is drawn at random from an ordinary deck of 52 cards, find the probability that it is:
a. Diamond
b. A red card
c. A heart or a spade
d. Not an ace
e. A black card or a king
4. The letters of the word HONESTY are written in slips of paper, and are placed in a box. A slip of paper is chosen at random. What is the probability that:
a. The letter is a vowel
b. The letter is a consonant
c. The letter is H

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. A coin is tossed thrice. What is the probability that at least 2 heads occur?
Since it's heads or tails, it's binomial.
P(at least 2 heads) = P(2 heads)+P(3 heads) = [3C2(1/2)2(1/2)=3(1/8)=3/8] +
[3C3(1/2)3(1/2)^0] = 1*1/8*1= 1/8 = 4/8= 1/2
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2. A pair of dice is rolled. What is the probability that the sum is equal to:
a. 5
The sample space has (1,4),(2,3),(3,2),(4,1)
P(5)= 4/36 = 1/9
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b. 10
The sample space has (4,6),(5,5),(6,4)
P(10)=3/36 = 1/12
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3. If a card is drawn at random from an ordinary deck of 52 cards, find the probability that it is:
a. Diamond: 13/52 = 1/4
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b. A red card: 26/52 = 1/2
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c. A heart or a spade: 13/52 + 13/52 = 26/52 = 1/2
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d. Not an ace; 1-P(ace) = 1 - 4/52 = 48/52
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e. A black card or a king: P(black)+P(king)-P(black and king)
=26/52 + 4/52 -2/52 = 28/52
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4. The letters of the word HONESTY are written in slips of paper, and are placed in a box. A slip of paper is chosen at random. What is the probability that:
a. The letter is a vowel: 2/7
b. The letter is a consonant: 5/7
c. The letter is H: 1/7
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Cheers,
Stan H.

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