Question

today's local newspaper lists 20 stocks of local interest. of those stocks ten increased five decreased and five remained unchanged yesterday. if wwe decide to buy two of stocks what is the likelyhood that both increased yesterday?

Answer 1

Answer:

P(x=2) = 0.2368

Step-by-step explanation:

given data

stocks of local interest N = 20

stocks increased K = 10

stocks decreased =  5

remained unchanged = 5

solution

we take here no of stock that are increased randomly n = 2

so here Hypergeometric random variable can take integer value

{max(0, n+k - N ), min(n,K) } = {0,2}

so here

P(x=2)

so

P(x=k)  = $\frac{(^K_k)\times (^{N-K}_{n-k}) }{(^N_n)}$      .......................1

P(x=2 ) = $\frac{(^{10}_2)\times (^{20-10}_{2-2}) }{(^{20}_2)}$    

solve it we get

P(x=2 ) = 0.236842

now we use excel function as

HYPGEOM.DIST (k,n,N.cumulative)   .....................2

so it will be

HYPGEOM.DIST (2,2,10,,false)

we get

HYPGEOM.DIST (2,2,10,,false)  = 0.236842

so

P(x=2) = 0.2368