seven dice are thrown simultaneously. Find the probability :
(i) of getting one four times
(ii) of one atleast three times
(iii) of getting three on four dices atleast
Answers
Answer:
The correct answer is 3)
Concept:
Probability can be defined as the ratio of favorable outcomes to the total possible outcomes.
Given:
Seven dice are thrown simultaneously.
Find:
The probability of getting one four times, of one at least three times, and of getting three on four dices at least.
Solution:
When Seven dice are thrown there are 6×6×6×6×6×6×6 = 6⁷, the number of possible outcomes.
(i) Getting one four times
Exactly four times 1 will come.
The favorable outcome, 1×1×1×1×5×5×5 = 125
Probability, P = 125/6⁷
(ii) Getting one at least three times
Getting 1 exactly three times + Getting 1 exactly four times + Getting 1 exactly five times + Getting 1 exactly six times + Getting 1 exactly seven times
The favorable outcome, 1×1×1×5×5×5×5 + 1×1×1×1×5×5×5 + 1×1×1×1×1×5×5 + 1×1×1×1×1×1×5 + 1×1×1×1×1×1×1 = 625 + 125 + 25 + 5 + 1 = 781
Probability, P = 781/6⁷
(ii) Getting three at least four times
Getting 3 exactly four times + Getting 3 exactly five times + Getting 3 exactly six times + Getting 3 exactly seven times
The favorable outcome, 1×1×1×1×5×5×5 + 1×1×1×1×1×5×5 + 1×1×1×1×1×1×5 + 1×1×1×1×1×1×1 = 125 + 25 + 5 + 1 = 156
Probability, P = 156/6⁷
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