PROBABILITY

• Finding Probability : Sum based on Geometric Figures

: Theorey question based on arguements

3m

2m

Q. Suppose you drop a die at random on the rectangular region shown in fig.

​

What is the probability that it will land inside the circle with diameter 1m?

Sol.

1m

.

Area of the rectangle =

l × b

= 3×2

= 6m²

For circle,

d = 1m,

∴ Area of the circle =

Favourable Area

∴ Total area = 6m²

∴ P(A) =

∴ P(A) =

Q. Which of the following arguments are correct and which are not correct? Give reasons for your answer.

(i) If two coins are tossed simultaneously there are three

each. Therefore, for each of these outcomes, the probability is

When two coins are tossed simultaneously,

All possible outcomes are HH, HT, TH, TT

No. of all possible outcomes

P (HH) =

P (TT) =

∴ P (HT or TH) =

possible outcomes - two heads, two tails or one of

Sol.

= 4

P (Two heads) =

∴ (i) argument is incorrect.

P (Two tails) =

P (one head or one tail) =

(ii) If a die is thrown, there are two possible outcomes –

an odd number or an even number. Therefore, the probability

of getting an odd number is

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When a die is thrown,

All possible outcomes are 1, 2, 3, 4, 5, 6

No. of all possible outcomes

P (odd number) =

∴ P (Even number) =

Sol.

= 6

∴ (ii) argument is correct.

P (1, 3, 5) =

P (2, 4, 6) =