six dice are thrown 729 times. how many times do you expect atleast 3 dice to show a five or a six?

1 Let the probability of occurrence of the event exactly in 3 dice be referred to as P (E, 3).

2 Let the event be, getting 4 or 5 when a die is thrown.

3 Probability of occurrence of the event in a single throw is p = 1 / 6 + 1 / 6= 1 / 3

4 q = 1 - p = 1 - 1 / 3= 2 / 3

5 Probability of occurrence of the event in at least 3 dice = P (E, 3) + P (E, 4) + P (E, 5) + P (E, 6)

6 This is a binomial situation and hence using the formula P (E, r) = nCr · pr · qn - r

7 The required probability = (6C3)(1 / 3)3 (2 / 3)3 + (6C4)(1 / 3)4(2 / 3)2 + (6C5)(1 / 3)5(2 / 3) + (6C6)(1 / 3)6

8 Required probability = (1 / 729) [(20 × 8) + (15 × 4) + (6 × 2) + 1] = 233 / 729
 [Simplify.]

9 Out of 729 throws, the number of times atleast 3 dice will show a 5 or 6 is 729 × 233 / 729 = 233.

10 So, we can expect at least 3 dice to show a 5 or 6 for 233 times

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 six dice are thrown 729 times. how many times do you expect atleast 3 dice to show a five or a six?

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 1.  Out of 100 balls 50 are red and the rest white. If 60 balls are picked at random, what is the probability of picking up:

a)  3 red balls?

b)  Not more than 3 red balls in the sample ?( e-3=0.0498)

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1. An urn initially contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and

it is replaced in the urn along with two other balls of the same color. Compute the probability that(a) one black and one white is selected.(b) exactly two black balls are selected.
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bag contains blue and red balls. Two balls are drawn randomly without replacement. The probability of selecting a blue and then a red ball is 0.2. The probability of selecting a blue ball in the first draw is 0.5. What is the probability of drawing a red ball, given that the first ball drawn was blue?
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Ftgfyu
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1/6+ 1/6 =1/3
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