Page 352 - Start Up Mathematics_8 (Non CCE)

Example 7: Find the probability that a leap year you selected at random will have 53 Tuesdays.
Solution: Let E be the event of selecting a leap year with 53 Tuesdays. A leap year has 366 days.

366 days = 52 weeks + 2 extra days
Thus, in a leap year 52 weeks will ensure 52 Tuesdays.
The remaining 2 days can be any of the following:
(a) Sunday and Monday (b) Monday and Tuesday

(c) Tuesday and Wednesday (d) Wednesday and Thursday
(e) Thursday and Friday (f) Friday and Saturday
(g) Saturday and Sunday
\ Total outcomes = 7
Out of these, the outcomes favourable to the event of having 53 Tuesdays are Monday and
Tuesday or Tuesday and Wednesday.
\ Favourable number of outcomes = 2
Favourable numberof outcomes 2
Hence, P(E) = =
Total outcomes 7

Example 8: Numbers 1 to 10 written on ten separate slips (one number on one slip) are kept in a box and
mixed well. One slip is chosen at random from the box without looking into it. What is the
probability of: (NCERT)
(a) getting a number 6? (b) getting a number less than 6?
(c) getting a 1-digit number?

Solution: There are 10 slips of paper with different numbers (i.e., 1 to 10) on it.
\ Total outcomes = 10
(a) Let A be the event of getting a number 6.
Favourable outcome = 1
Favourable outcomes 1
\ P(A) = =
Total outcomes 10
(b) Let B be the event of getting a number less than 6, i.e., 1, 2, 3, 4 and 5.

Favourable outcome = 5
Favourable outcomes 5 1
\ P(B) = = =
Total outcomes 10 2
(c) Let D be the event of getting a 1-digit number, i.e., 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Favourable outcomes = 9
Favourable outcomes 9
\ P(D) = =
Total outcomes 10

Example 9: A box contains 20 eggs out of which 8 are defective. One egg is taken out at random from
the box. What is the probability that the egg is not defective?

Solution: Total number of eggs in the box = 20
Number of defective eggs = 8
Number of non-defective eggs = 20 – 8 = 12
Number of non-defectiveeggs 12 3
\ P (Not a defective egg) = = =
Total numberofeggs 20 5

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