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A die is thrown, find the probability of following events :
(i) A prime number will appear.
(ii) A number greater than or equal to 3 will appear.
(iii) A number less than or equal to one will appear.
(iv) A number more than 6 will appear.
(v) A number less than 6 will appear.
(i) A prime number will appear.
(ii) A number greater than or equal to 3 will appear.
(iii) A number less than or equal to one will appear.
(iv) A number more than 6 will appear.
(v) A number less than 6 will appear.
Solution:
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Verified Answer
In this case, the possible outcomes are $1,2,3,4,5$ and 6.
Total number of possible outcomes $=6$.
(i) Number of outcomes favourable to the event
"a prime number" $=3($ i.e., 2, 3, 5)
$P($ prime number $)=\frac{3}{6}=\frac{1}{2}$
(ii) Number of outcomes favourable to the event "a number greater than or equal to $3^{\prime \prime}=4$ (i.e., 3, 4, $5,6)$
$P($ a number greater than or equal to 3 ) $=\frac{4}{6}=\frac{2}{3}$
(iii) Number of outcomes favourable to the event. "a number less than or equal to one" $=1$ (i.e., 1).
$P($ a number less than or equal to one $)=\frac{1}{6}$
(iv) Number of outcomes favourable to the event "a number more than $6^{\prime \prime}=0$
$P($ a number more than 6$)=\frac{0}{6}=0$
(v) Number of outcomes favourble to the event "a number less than $6^{\prime \prime}=5$ (i.e., 1, 2, 3, 4,5)
$P($ a number less than 6$)=\frac{5}{6}$
Total number of possible outcomes $=6$.
(i) Number of outcomes favourable to the event
"a prime number" $=3($ i.e., 2, 3, 5)
$P($ prime number $)=\frac{3}{6}=\frac{1}{2}$
(ii) Number of outcomes favourable to the event "a number greater than or equal to $3^{\prime \prime}=4$ (i.e., 3, 4, $5,6)$
$P($ a number greater than or equal to 3 ) $=\frac{4}{6}=\frac{2}{3}$
(iii) Number of outcomes favourable to the event. "a number less than or equal to one" $=1$ (i.e., 1).
$P($ a number less than or equal to one $)=\frac{1}{6}$
(iv) Number of outcomes favourable to the event "a number more than $6^{\prime \prime}=0$
$P($ a number more than 6$)=\frac{0}{6}=0$
(v) Number of outcomes favourble to the event "a number less than $6^{\prime \prime}=5$ (i.e., 1, 2, 3, 4,5)
$P($ a number less than 6$)=\frac{5}{6}$
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