My probability question #1 (1 Viewer)

[snoopy05]

a box contains 10 chocolates. three of the chocolates have caramel centers, and other 7 has mint centers. hugo selects 3 chocolate from the box randomly,

what is the probability that hugo eats atleast 2 caramel chocolates


the answer is 11 / 60

(how can we do this without using tree diagram?)
or is it best for us to use tree diagram? .....(assume that i dont have the ability to visualise things very good)

 

[SaHbEeWaH]

P(selects 2 caramel chocolates): ³/₁₀ * ²/₉ * ⁷/₈ * ³C₂ = ⁷/₄₀

P(selects 3 caramel chocolates): ³/₁₀ * ²/₉ * ¹/₈ = ¹/₁₂₀

Therefore, P(selects at least 2 caramel) = ⁷/₄₀ + ¹/₁₂₀ = ¹¹/₆₀

or ...

P(selects no caramel chocolates): ⁷/₁₀ * ⁶/₉ * ⁵/₈ = ⁷/₂₄

P(selects 1 caramel chocolate): ⁷/₁₀ * ⁶/₉ * ³/₈ * ³C₁ = ²¹/₄₀

Therefore, P(selects at least 2 caramel) = 1 - ⁷/₂₄ - ²¹/₄₀ = ¹¹/₆₀