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a bed of flowers consists of $100$ stalks of flowers of which $20$ are lillies, $h$ are roses and the rest are tulips. given that the probability of picking a stalk of tulip at random is $\frac{1}{4}$ find the value of $h$ .

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Probability of independent and dependent events

Full solution

Q. a bed of flowers consists of

100

stalks of flowers of which

20

are lillies,

h

are roses and the rest are tulips. given that the probability of picking a stalk of tulip at random is

\frac{1}{4}

find the value of

h

.

Total Flowers Calculation: Total number of flowers = $100$ Number of lilies = $20$ Number of tulips = Probability of tulip $\times$ Total number of flowers Number of tulips = $\frac{1}{4} \times 100 = 25$
Number of Tulips Calculation: Now, let's find the number of roses, $h$ . $\newline$ Total flowers = Number of lilies + Number of tulips + Number of roses $\newline$ $100 = 20 + 25 + h$
Number of Roses Calculation: Solve for $h$ : $100 = 45 + h$ $h = 100 - 45$ $h = 55$

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